Theorem 3com12d 34499

Description: Commutation in consequent. Swap 1st and 2nd. (Contributed by Jeff Hankins, 17-Nov-2009.)

Hypothesis

Ref	Expression
3com12d.1	⊢ (𝜑 → (𝜓 ∧ 𝜒 ∧ 𝜃))

Assertion

Ref	Expression
3com12d	⊢ (𝜑 → (𝜒 ∧ 𝜓 ∧ 𝜃))

Proof of Theorem 3com12d

Step	Hyp	Ref	Expression
1		3com12d.1	. 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒 ∧ 𝜃))
2		id 22	. . 3 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜓 ∧ 𝜃))
3	2	3com12 1122	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → (𝜒 ∧ 𝜓 ∧ 𝜃))
4	1, 3	syl 17	1 ⊢ (𝜑 → (𝜒 ∧ 𝜓 ∧ 𝜃))

Syntax hints:   → wi 4   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1088

This theorem is referenced by: (None)